| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | November |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Particle on rough incline, particle hanging |
| Difficulty | Standard +0.3 This is a standard M1 pulley-on-incline problem requiring resolution of forces, Newton's second law for connected particles, and friction calculations. The geometry is straightforward (3-4-5 triangle), and the method is routine: draw forces, apply F=ma to both particles, use F=μR, then solve simultaneous equations. Slightly above average due to the multi-step nature and friction component, but follows a well-practiced template with no novel insight required. |
| Spec | 3.03e Resolve forces: two dimensions3.03k Connected particles: pulleys and equilibrium3.03l Newton's third law: extend to situations requiring force resolution3.03v Motion on rough surface: including inclined planes |
\includegraphics{figure_7}
A rough inclined plane of length 65 cm is fixed with one end at a height of 16 cm above the other end. Particles $P$ and $Q$, of masses $0.13$ kg and $0.11$ kg respectively, are attached to the ends of a light inextensible string which passes over a small smooth pulley at the top of the plane. Particle $P$ is held at rest on the plane and particle $Q$ hangs vertically below the pulley (see diagram). The system is released from rest and $P$ starts to move up the plane.
\begin{enumerate}[label=(\roman*)]
\item Draw a diagram showing the forces acting on $P$ during its motion up the plane. [1]
\item Show that $T - F > 0.32$, where $T$ N is the tension in the string and $F$ N is the magnitude of the frictional force on $P$. [4]
\end{enumerate}
The coefficient of friction between $P$ and the plane is 0.6.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Find the acceleration of $P$. [6]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2007 Q7 [11]}}